We numerically study the structure and the normal-mode spectrum of two vertically coupled finite-size two-dimensional systems of interacting classical charged particles that are confined by a nonuniform distribution of background charge. The structural and dynamical properties of the system are analyzed as a function of the separation between the planes of charges $\left(d\right)$, as well as a function of the strength of the confinement potential $\left(Z\right)$. We find different asymmetrical ground-state configurations, as well as structural phase transitions induced by the unbinding of particles, which were not present in previous models with a parabolic confinement potential. Depending on the order of the structural transition the normal-mode frequencies exhibit a discontinuity or a softening.

• Received 20 February 2007

DOI:https://doi.org/10.1103/PhysRevB.76.035336